Session E14: Graphene: Transport Properties

Fermi surface anisotropy of graphene measured by ballistic transport experiments on antidot lattice samples

Monolayer graphene and bilayer graphene have strikingly different properties. One such difference is the shape of the Fermi surface. Although anisotropic band structures can be detected in optical measurements, they have so far been difficult to detect in transport experiments on two-dimensional materials. Here we describe a ballistic transport experiment using high-quality graphene that revealed Fermi surface anisotropy in the magnetoresistance. The shape of the Fermi surface is closely related with the cyclotron orbit in real space. Electron trajectories in samples with triangular lattices of holes depend on the anisotropy of the Fermi surface. We found that this results in the magnetoresistance which are dependent on crystallographic orientation of the antidot lattice, which indicates the anisotropic Fermi surface of bilayer graphene which is a trigonally-warped circle in shape. While in monolayer, shape of magnetoresistance was approximately independent of the orientation of antidot lattice, which indicates that the Fermi surface is a circle in shape.   

Universal voltage scaling due to self-averaging of quantum corrections in graphene

The differential conductance of graphene is shown to exhibit a zero-bias anomaly at low temperatures, arising from a suppression of the quantum corrections due to weak localization and electron interactions. A simple rescaling of these data, free of any adjustable parameters, shows that this anomaly exhibits a universal, temperature independent form. According to this, the differential conductance is approximately constant at small voltages (V<k_BT/e), while at larger voltages it increases logarithmically with the applied bias, reflecting a quenching of the quantum corrections. For theoretical insight into the origins of this behavior, we formulate a model for weak-localization in the presence of nonlinear transport. According to this, the voltage applied under nonequilibrium induces unavoidable dephasing, arising from a self-averaging of the diffusing electron waves responsible for transport. By establishing the manner in which the quantum corrections are suppressed in graphene, our study will be of broad relevance to the investigation of nonequilibrium transport in mesoscopic systems in general. This includes systems implemented from conventional metals and semiconductors, as well as those realized using other two-dimensional semiconductors and topological insulators.   

Uniform doping of graphene close to the Dirac point by polymer-assisted assembly of molecular dopants

Tuning the charge carrier density of two-dimensional (2D) materials by incorporating dopnats into the crystal lattice is a challenging task. An attractive alternative is the surface transfer doping by adsorption of molecules on 2D crystals, which can lead to ordered molecular arrays. However, such systems, demonstrated in ultra-high vacuum conditions (UHV), are often unstable in ambient conditions. Here we show that air-stable doping of epitaxial graphene on SiC-achieved by spin-coating deposition of 2,3,5,6-tetrafluoro-tetracyano-quino-dimethane (F4TCNQ) incorporated in poly(methyl-methacrylate)-proceeds via the spontaneous accumulation of dopants at the graphene-polymer interface and by the formation of a charge-transfer complex that yields low-disorder, charge-neutral, large-area graphene with carrier mobilities ~70,000cm²V^-1s^-1 at cryogenic temperatures. The assembly of dopnats on 2D materials assisted by a polymer matrix, demonstrated by spin-coating wafer-scale substrates in ambient conditions, opens up a scalable technological route toward expanding the functionality of 2D materials.
Reference: Hans He et. al., Nature Communication 9, 3956 (2018)   

Thermal broadening in graphene-based electromechanical nanosensors and molecular electronic junctions.

New nanoscale devices and protocols for molecular detection in aqueous environments at room temperature are highly desirable for their potential application in DNA sequencing and in vivo cell studies. Due to their electromechanical properties, graphene and other 2D materials provide a platform for electromechanical sensing under these conditions. We have investigated this idea by analyzing representative models. In particular, we have derived analytic expressions for the current, the electromechanical susceptibility, and signal-to-noise ratio. These expressions reveal the relative importance of thermal fluctuations, strain and geometric properties in the electromechanical response. Significantly, we find that as a result of the environmental fluctuations, electromechanical structures have an electron transmission function that follows a generalized Voigt profile, in close analogy to the inhomogeneous lineshapes found in spectroscopic and diffraction studies. These results allow us to formulate sensing protocols in terms of detector parameters, and give the fundamental operational principles for graphene deflectometry.   

Excitons beyond the effective mass approximation: application to biased bilayer graphene

In conventional semiconductors, the exciton bound state (arising from the attractive Coulomb interaction between electrons and holes) can be successfully analyzed by the effective mass approximation based on the lowest-order parabolic dispersion relation at band extrema. However, parabolic dispersion is by no means the only possible outcome endowed by a periodic lattice potential, especially in two dimensional electronic materials, where weak inter-subband matrix elements suppress otherwise strong band repulsion across a forbidden gap, resulting in nonparabolic ‘Mexican hat’ or ‘caldera’-shaped bands, in which “effective mass” is ill-defined. Focusing on electrostatically-biased bilayer graphene as an example where quartic (and higher) dispersion terms are necessary, we present a semi-analytic theory used to investigate the properties of ground and excited excitonic states. This includes determination of the exciton binding energy and wavefunctions, which are further used to analyze the relative oscillator strengths and magnetic moments (g-factors) that can be directly compared to recent experimental measurements.   

Theory of thermoelectric transport in bilayer graphene

We present a simple theory of thermoelectric transport in bilayer graphene and report our results for the electrical resistivity, the thermal resistivity, and the Wiedemann-Franz (WF) ratio as functions of doping density and temperature. In contrast with monolayer graphene we obtain finite electrical and thermal resistivities, even in the absence of disorder, i.e. in the extreme hydrodynamic regime. The WF ratio of the clean system reaches a maximal value at the charge-neutrality-point (CNP), and this value increases as a function of temperature. This is in contrast with a perfectly clean monolayer graphene where the WF ratio becomes infinite in the absence of disorder (requiring disorder to be observable).
When disorder is included, we find that the WF ratio in bilayer graphene drops below its maximal value, resulting in an interesting non-monotonic behavior as a function of doping density in the vicinity of the CNP.   

Quantum limit of thermal conductance in Graphene

In condensed matter physics, last one decade, the graphene, a single carbon atomic layer, has emerged as an ideal platform to experimentally verify many theoretical predictions. One of those predictions are to see the quantum limit of electrical conductance as well as thermal conductance. Although the quantization of electrical conductance (in e²/h) has been observed in graphene quantum Hall (QH) but the demonstration of quantization of thermal conductance in terms of its quantum limit (p²k_b²/3h T) remains challenging due to the requirement of accurate measurement of very small temperature change. The quantum limit of thermal conductance has been demonstrated recently in GaAs-AlGaAs heterostructures but its determination in graphene QH will open a new path to study the unique exotic phases near the Dirac point, which can be uniquely identified by the thermal conductance measurements. Motivated by this we have carried out the thermal conductance measurement in the integer QH regime of graphene by sensitive noise thermometry setup. We have measured the thermal conductance for n =1, 2 and 6 plateaus and its values agree with the quantum limit of it by more than 95% accuracy.   

Breakdown of the law of reflection at a disordered graphene edge

The law of reflection states that smooth surfaces reflect waves specularly, thereby acting as a mirror. This law is insensitive to disorder as long as its length scale is smaller than the wavelength. Monolayer graphene exhibits a linear dispersion at low energies and consequently a diverging Fermi wavelength. We present proof that a charge-neutral disordered graphene boundary results in a diffusive electron reflection even when the electron wavelength is much longer than the disorder correlation length. Using numerical quantum transport simulations, we demonstrate that this phenomenon can be observed as a nonlocal conductance dip in a magnetic focusing experiment.   

Ultrafast Valley polarization in gapped graphene

We study numerically the ultrafast valley polarization in gapped graphene that can be accessed and controlled by a single cycle of a circularly polarized intense pulse. The amplitude of the pulse is about 0.5 V/\AA and its duration is 5 fs. Depending on the polarization of the pulse, right or left handed, one valley, K or K’, is significantly populated, resulting in significant residual valley polarization of gapped graphene. The unequal valley population in the reciprocal space is due to topological resonance, which is caused by the mutual cancellation of the topological and dynamic phases. The ultrafast valley polarization, generated in gapped graphene-like materials, can be used in ultrafast quantum memory devices.   

All-Electronic Thermal Transport With Nonlocal Noise Thermometry in Graphene

Ever since the measurements of Wiedemann and Franz in 1853, thermal transport has played a central role in condensed matter physics. Thermal conductance can help pinpoint neutral modes such as spin waves, non-Fermi liquid states such as hydrodynamic states and Luttinger liquids, and topological degrees of freedom such as Majorana modes. In this context, van der Waals materials now offer a rich landscape of interacting, symmetry-broken, and topological states of matter enhanced by their low dimensionality, yet thermal transport has remained a difficult probe to realize for few-atom thick materials and for many of the most delicate electronic ground states. Here, we demonstrate a new technique to achieve all-electronic thermal transport in a van der Waals material. We use graphene as a sensitive electronic heater and thermometer by implementing a new type of nonlocal noise thermometry. We show that the technique allows us to accurately extract the electronic thermal conductance of a bridge between two graphene thermometers. This new probe now allows us to study a wide array of symmetry-broken and topological states in van der Waals materials through their heat transport properties.   

Studying the effects of strain in graphene using a MEMS device and electronic transport measurements at low temperatures

Different theoretical studies have motivated experiments on strained graphene, predicting exotic behaviors such as superconductivity or the induction of gauge fields that act effectively as large magnetic fields. Up to now the study of strain in graphene has been limited to the use of substrates where wrinkles or bubbles create strain or to the use of flexible substrates that create strain when they are bent. Here we present preliminary electronic transport experiments at low temperatures on a suspended graphene where strain is applied through a sophisticated micro-electro-mechanical systems (MEMS). We observe features in the magnetoresistance that change as strain is imposed to the sample, possibly showing the effects of the superposition of a magnetic field and a time reversal symmetric pseudo-magnetic field.   

Ballistic Transport of Epitaxial Graphene Nanoribbons on SiC

Exceptional ballistic transport was observed in sidewall epitaxial graphene nanoribbons on SiC (SWGNRs) at room temperature [1]. These objects are of fundamental interest as they provide a direct access to charge neutral graphene with excellent transport properties. Here, beyond sidewalls, we fabricate epitaxial graphene nanoribbons on different crystal faces on SiC, including Si-face and non-polar facets. We introduce amorphous carbon as contact pads and high temperature annealing to reduce the edge roughness of ribbons and the contamination from resist residue. Then we discuss transport measurment and magnetoresistance results of graphene nanoribbons on Si-face as well as on non-polar SiC facets, which might reveal the nature of the ballistic channels in SWGNRs.
[1] J. Baringhaus et al. Nature 506, 349 (2014).   

Electron-phonon Cerenkov instability in graphene revealed by global and local noise measurements

Understanding and controlling non-equilibrium electronic phenomena is an outstanding challenge in science and engineering. Graphene presents a particularly interesting system for studying such effects because its high mobility means electrons may be accelerated very far out of equilibrium. We find that when fully encapsulated graphene is driven with a sufficiently high DC current, the drift velocity of the electrons exceeds the phase velocity of sound. This results in population inversion of the electronic system and stimulated emission of phonons becomes the dominant scattering process. This phonon Cerenkov effect leads to a runaway growth of certain phonon modes in the direction of momentum flow. Using NV centers as local noise probes, we map the exponential spatial growth of the phonon population by measuring the resulting local current fluctuations. Additionally, we measure a significantly altered global noise spectrum and AC conductivity at GHz frequencies, both of which are well described by stimulated emission of acoustic phonons. Since the amplified phonons are primarily in the THz range, the observation of a phonon Cerenkov effect in graphene is a first step towards realizing an on-chip generator of THz sound and radiation.   

Elastic response of the electron fluid in intrinsic graphene: The collisionless regime

The elastic response of an electron fluid at finite frequencies is defined by the electron viscosity η(ω). We determine η(ω) for graphene at the charge neutrality point in the collisionless regime, including the leading corrections due to the electron-electron Coulomb interaction. We find interaction corrections to η(ω) that are significantly larger if compared to the corresponding corrections to the optical conductivity. In addition, we find comparable contributions to the dynamic momentum flux due to single-particle and many-particle effects. We also demonstrate that η(ω) is directly related to the nonlocal energy-flow response of graphene at the Dirac point. The viscosity in the collisionless regime is determined with the help of the strain generators in the Kubo formalism. Here, the pseudospin of graphene describing its two sublattices plays an important role in obtaining a viscosity tensor that fulfills the symmetry properties of a rotationally symmetric system.